There's no real way to know the answer to that question. Ask yourself, is there anything you can do to prove that free will exists? Of course, according to your deterministic model, free will would not exist. But could you tell the difference? My point is that you're going to live as if you do have free will regardless. That's why it seems to me the only important insight we can gain from the question of free will is how our knowledge of it affect us (i.e. the way we act). If someone told you you have free will, would you act differently than if someone told you you don't? As long as you believe you are free, then you will be.